3-2/9b=b-7

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Solution for 3-2/9b=b-7 equation:



3-2/9b=b-7
We move all terms to the left:
3-2/9b-(b-7)=0
Domain of the equation: 9b!=0
b!=0/9
b!=0
b∈R
We get rid of parentheses
-2/9b-b+7+3=0
We multiply all the terms by the denominator
-b*9b+7*9b+3*9b-2=0
Wy multiply elements
-9b^2+63b+27b-2=0
We add all the numbers together, and all the variables
-9b^2+90b-2=0
a = -9; b = 90; c = -2;
Δ = b2-4ac
Δ = 902-4·(-9)·(-2)
Δ = 8028
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{8028}=\sqrt{36*223}=\sqrt{36}*\sqrt{223}=6\sqrt{223}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{223}}{2*-9}=\frac{-90-6\sqrt{223}}{-18} $
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{223}}{2*-9}=\frac{-90+6\sqrt{223}}{-18} $

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